Problem 44 Solve each equation: $$ -3 x... [FREE SOLUTION]

Chapter 7: Problem 44

Solve each equation: $$ -3 x+3=18 $$

Short Answer

Expert verified

The solution is $x = -5$.

Step by step solution

Isolate the Variable Term

Start with the equation $-3x + 3 = 18$. To isolate the term with $x$, we should first remove the constant on the left side. Subtract 3 from both sides: $-3x + 3 - 3 = 18 - 3$. This simplifies to $-3x = 15$.

Solve for the Variable

Now, we have the equation $-3x = 15$. To solve for $x$, divide both sides by $-3$: $x = \frac{15}{-3}$. This simplifies to $x = -5$.

Verify the Solution

Substitute $x = -5$ back into the original equation to verify: $-3(-5) + 3 = 18$. Simplify: $15 + 3 = 18$, which is correct. Hence, $x = -5$ is the correct solution.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Isolating Variables

In the journey of solving linear equations, one of the foundational steps is isolating the variable. Let's consider our equation: $-3x + 3 = 18$. The goal here is to get $x$ by itself on one side. We achieve this by removing all other numbers from the $x$ term's side. Here's how you can think about it:

Identify the constant term next to $x$, which is $+3$ in our case.
To remove this $+3$, we subtract 3 from both sides. This keeps the equation balanced.
So, $-3x + 3 - 3 = 18 - 3$
This simplifies the equation to just the $x$ term: $-3x = 15$

By isolating $-3x$, you've cleared the path to focus on finding the value of $x$. Remember, keeping the equation balanced is crucial when moving terms around.

Solving Equations

After successfully isolating the variable term, the next step is solving for $x$. This involves narrowing down the equation to one simple answer. With the equation now at:$-3x = 15$Here鈥檚 how you approach it:

The coefficient of $x$ is $-3$. To "cancel out" this $-3$ and just find $x$, divide everything by $-3$:
$x = \frac{15}{-3}$
Perform the division. When we divide 15 by $-3$, we find:
$x = -5$

The equation has been solved, and $x$ equals $-5$. Solving equations often feels like solving a puzzle 鈥� everything must fit perfectly to reach the final answer.

Verifying Solutions

Finally, we must confirm that our solution is indeed the correct one. Verification is a step often skipped but crucial for ensuring accuracy.
Here's how you do it with the solution $x = -5$:

Go back to the original equation and substitute $-5$ for $x$:$-3(-5) + 3 = 18$
Simplify the expression:
$15 + 3 = 18$
Check that both sides of the equation are equal.
Since they are, this confirms $x = -5$ is the correct solution.

Verifying solutions not only boosts your confidence but also ensures your solution isn't just theoretically but also practically correct.

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91影视

Solve each equation: $$ -3 x+3=18 $$

Short Answer

Step by step solution

Isolate the Variable Term

Solve for the Variable

Verify the Solution

Key Concepts

Isolating Variables

Solving Equations

Verifying Solutions

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